How does a catalyst speed up a chemical reaction

By being an alternative route to the reaction with a lower activation energy.

Answer: by lowering the activation energy.

Explanation:

Activation energy is the extra energy that must be supplied to reactants in order to cross the energy barrier and thus convert to products.

A catalyst is a substance which increases the rate of a reaction by taking the reaction through a different path which involves lower activation energy and thus more molecules can cross the energy barrier and convert to products.

The catalyst itself does not take part in the chemical reaction and is regenerated as such at the end.